Rotation Numbers, Boundary Forces and Gap labelling

We review the Johnson-Moser rotation number and the $K_0$-theoretical gap labelling of Bellissard for one-dimensional Schr\"odinger operators. We compare them with two further gap-labels, one being related to the motion of Dirichlet eigenvalues, the other being a $K_1$-theoretical gap label. We argue that the latter provides a natural generalisation of the Johnson-Moser rotation number to higher dimensions.Comment: 10 pages, version accepted for publicatio

Seasonal changes in physical capacities of basketball players according to competitive levels and individual responses

PURPOSE:The aim of this study was to quantify changes in physical capacities of thirty-eight basketball players selected from different teams, as well as from varying competitive levels (i.e. Division I, Division II and Division III) during the preparation and in-season periods. METHODS:Pre (T1) and post (T2) preparation period and during regular season (T3), the players completed a Yo-Yo Intermittent Recovery test-level 1. Following a 3 to 8 days-break, players performed a 6-min continuous running test (Mognoni's test), a counter-movement jump test and a 5-min high-intensity intermittent running test. RESULTS:Blood lactate concentration measured after the Mognoni's test was significantly reduced from T1 to T2, and from T2 to T3 (P<0.001, ƞ2 = 0.424). The distance covered during the Yo-Yo Intermittent Recovery test was significantly increased only from T1 to T2 in Division II and III (P<0.001, ƞ2 = 0.789). Similarly, the physiological responses to high-intensity intermittent running test were improved only from T1 to T2 (all P<0.001, ƞ2 = 0.495 to 0.652). Despite significant changes observed in running tests from T1 to T2, at individual level 35-55% of players did not show a very likely improvement. Relative peak power produced during vertical jumps at T3 by Division I players was increased compared to T1 (ANOVA interaction, P = 0.037, ƞ2 = 0.134). CONCLUSIONS:The main improvements in physical capacities occurred during the preparation period, when the aerobic fitness and the ability to sustain high-intensity intermittent efforts were moderately-to-largely improved. However, it appears that the preparation period does not consistently impact on vertical jump variables. Aerobic fitness and force/power production during vertical jumps appear to improve across the competitive season (slightly-to-moderately). Physical tests should be used to identify weaknesses in physical performance of players and to monitor their fatigue status, with the aim to develop individualized training programs

Quantum Metrology: Towards an alternative definition for the meter

The motivation for this article came from an attempt to give an alternative definition for the meter, the SI unit for measuring length. As a starting point towards this goal, in this piece of work we present the underlying theory behind our approach which uses ideas from quantum field theory and noncommutative geometry, in particular the notion of an odd K-cycle which is based on the Dirac operator (and its inverse, the Dirac propagator). Using (the perhaps more familiar) physics terminology, the key point in our strategy is this: instead of measuring length directly in space-time we measure the "algebraic (spectral) length" in the space of the corresponding quantum states of some particle (fermion) acted upon by the Dirac propagator. This approach shares the spirit of the unanimus vote of the 24th General Conference of Standards and Measures (21st October 2011) in Serves, France for the redefinition of the fundamental units using Planck's constant.Comment: Extended version of an invited talk during the 4th Tactical Conference on Metrology, 3-4 February 2012, National Technical University of Athens, Athens Greec

Neutrino and Antineutrino Inclusive Charged-current Cross Section Measurements with the MINOS Near Detector

The energy dependence of the neutrino-iron and antineutrino-iron inclusive charged-current cross sections and their ratio have been measured using a high-statistics sample with the MINOS Near Detector exposed to the NuMI beam from the Main Injector at Fermilab. Neutrino and antineutrino fluxes were determined using a low hadronic energy subsample of charged-current events. We report measurements of neutrino-Fe (antineutrinoFe) cross section in the energy range 3-50 GeV (5-50 GeV) with precision of 2-8% (3-9%) and their ratio which is measured with precision 2-8%. The data set spans the region from low energy, where accurate measurements are sparse, up to the high-energy scaling region where the cross section is well understood.Comment: accepted by PR